Coherent, Efficient and Practical Polariton Lasers Using a Designable Cavity

September 1, 2022

Army Research Laboratory, Adelphi, Maryland

Figure 1. Left, Second-order auto-coherence function gg ⁽²⁾(0) vs. the normalized excitation power. It measures the intensity noise of the polariton laser, which shows a sharp decrease above the threshold to the shot-noise limit of 1. Large fluctuations around the threshold reflects relaxation oscillation. The blue (red) data correspond to pulsed (continuous wave) excitation. The inset is the corrected for the time-resolution of the photo detectors and the blue line is a theoretical fit. The grayed area corresponds to weak-coupling regime. Right: Phase coherence time vs. the polariton number in the lasing mode. It is obtained from first-order coherence measurements. A sharp increase of the coherent time was seen near threshold as expected in typical lasers. The decrease of the coherence time at large polariton number, while maintaining shot-noise limited intensity noise, results from interactions among polaritons in the lasing mode.

Coherence properties are what distinguish a laser from other sources of light and make it useful. This research demonstrates for the first time a polariton laser with coherence reaching the intrinsic limit of single-mode matter-wave lasers. It further demonstrates intensity coherence at the shot-noise limit expected of an ideal coherent state (Figure 1, left), and phase coherence revealing interactions within the polariton condensate due to its matter-wave nature (Figure 1, right).

This research also demonstrates a new mechanism of frequency comb generation using coupled polariton condensates. It results from the dynamic interplay between on-site nonlinearity and inter-site couplings. This is distinct from other systems, such as microtoroidal resonators and quantum cascade lasers that are based on cascaded four-wave mixing process. A unique feature of this form of frequency comb generation is that the comb spacing is not given by the cavity transverse mode spacing and can be engineered from GHz to THz without having to drastically change the physical dimension of the system. Furthermore, since it is based on polariton condensation, the polariton comb allows a very low threshold and an incoherent pump, including electrical injection.

Figure 2. (a) A bifrucation diagram of the coupled polariton system in the parameter space of pump rate vs. dissipation coupling rate γγ, normalized by the cavity decay rate Γ . The standard lasing threshold is when /Γ = 1 in the absence of dissipative coupling. For finite dissipation γγ, thresholds for stable and unstable fixed-point solutions emerge with increasing pump, as indicated by the arrow. (b) The real space spectrum showing bifurcation from the bonding and anti-bonding states into four frequencies as marked by the solid white lines. All four frequencies are well below and distinct from the next excited state of the cavity system as marked by the white dashed line. (c) Time-domain first order coherence from the two sites (red and blue symbols denotes the left and right site respectively). Both sites show oscillations due to the multiple frequency components and agree well with simulations (not shown here). (d) Measurement of the relative phase between the two sites by spatial interference with a reference beam. (e) Fringes obtained from (d) for the two sites (red and blue symbols respectively), showing both different intensities and a relative phase displacement of *ΔØØ* =0.51 ± 0.08 ϖϖ, as expected for the frequency comb state. In contrast, stable bonding or anti-boding state lasing should feature equal intensity between the two sites and a phase difference of *ΔØØ* = 0 or ϖϖ, as observed at lower or higher pump rates (not shown here).

The matter-wave frequency comb is created using the designable HPCC cavity with a suspended high-contrast grating mirror, which allows the creation of two coupled condensate, as well as engineering their interaction and coupling via deformation of the suspended mirrors. Extensive experimental and theoretical evidence was obtained to support the results, including spectroscopy and interferometric measurements showing equidistant frequency lines and characteristic phase relations between the two coupled condensates (Figure 2).

This work paves the way for future development and optimization of low threshold optical frequency comb sources and will open doors to other novel phenomena and device concepts based on dissipatively-coupled nonlinear cavity systems.

This research also demonstrated the first polariton laser in the Bardeen-Coo-per-Schrieffer (BCS) regime, which is also the first demonstration of the particle-hole type BCS state as well as matter-light hybrid BCS state. It validates and pushes forward many decades of theoretical efforts on this subject.

Both the BEC and BCS states were postulated in excitonic systems half a century ago. Research on exciton- and especially polariton-BEC has exploded recently, with a large part of the community accepting spectral features as experimental evidence of a polariton BEC despite persistent skepticism. BCS has been considered much more difficult to achieve, and no experimentally accessible hallmark signatures have been identified.

In the HPCC polariton system, both the weakly and strongly cavity-cou-pled excitons coexist and share the same hot carrier reservoir, enabling access to the electronic media at the presence of polariton lasing. In what would have been commonly accepted as a polariton BEC, fermionic gain and population inversion (Figure 3) were measured directly, unambiguously distinguishing it from a polariton BEC. Stark contrast in spectral properties between the BCS polariton laser and a conventional photon laser were also shown, thereby unambiguously distinguishing it from the commonly known photon laser. A theory based on extended semiconductor Bloch equation reproduces the experimental results and in turn reveals the BCS nature of the new many-body phase.

Figure 3. Gain and energetic positions of a BCS polariton laser. (a) Reflection/absorption spectra of the electronic reservoir at different pump powers, showing clearly gain, above the reference level of unity marked by the black lines. Inset: zoom-in near the gain. (b) Pump power dependence of the energetic positions of the polariton ground state (red squares), the exciton (solid blue circles) and upper spectral-bound of gain (grey triangles). The BCS polariton lasing threshold (black dashed line) coincides with the onset of the fermionic gain.

These findings challenge the previous understanding and experimental interpretation of polariton BEC while at the same time reconfirming that strong electronic correlations underline phenomena so far associated with polariton BEC.

This work was performed by Hui Deng of the Regents of the University of Michigan for the Air Force Research Laboratory. For more information, download the Technical Support Package (free white paper) at mobilityengineeringtech.com/tsp under the Optics, Photonics & Lasers category. AFRL-0308